Radha made a picture of an aeroplane with coloured paper as shown in Fig. Find the total area of the paper used.
Radha made a picture of an aeroplane with coloured paper as shown in Fig. Find the total area of the paper used.
For the triangle I section:
It is an isosceles triangle and the sides are 5 cm, 1 cm and 5 cm
Perimeter = 5 + 5 + 1
= 11 cm
So, semi perimeter = 11/2 cm
= 5.5 cm
Using Heron’s formula,
Area = \(\sqrt{s(s - a)(s - b)(s - c)}\)
= √[5.5(5.5- 5)(5.5-5)(5.5-1)] cm2
= √[5.5×0.5×0.5×4.5] cm2
= 0.75√11 cm2
= 0.75 × 3.317 cm2
= 2.488 cm2 (approx)
For the quadrilateral II section:
This quadrilateral is a rectangle with length and breadth as 6.5 cm and 1 cm respectively.
∴ Area = 6.5 × 1 cm2 = 6.5 cm2
For the quadrilateral III section:
It is a trapezoid with 2 sides as 1 cm each and the third side as 2 cm.
Area of the trapezoid = Area of the parallelogram + Area of the equilateral triangle
The perpendicular height of the parallelogram will be
= \(\sqrt{1^2 - (0.5)^2}\)
= 0.86 cm
And, the area of the equilateral triangle will be (√3/4 × a2) = 0.43
∴ Area of the trapezoid = 0.86 + 0.43
= 1.3 cm2 (approximately).
For triangle IV and V:
These triangles are 2 congruent right angled triangles having the base as 6 cm and height 1.5 cm
Area triangles IV and V = 2 × (1/2 × 6 × 1.5) cm2
= 9 cm2
So, the total area of the paper used = (2.488 + 6.5 + 1.3 + 9) cm2
= 19.3 cm2
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